docs: def API520_F2(k, P1, P2):
      r'''Calculates coefficient F2 for subcritical flow for use in API 520
      subcritical flow relief valve sizing.
  
      .. math::
          F_2 = \sqrt{\left(\frac{k}{k-1}\right)r^\frac{2}{k}
          \left[\frac{1-r^\frac{k-1}{k}}{1-r}\right]}
  
      .. math::
          r = \frac{P_2}{P_1}
  
      Parameters
      ----------
      k : float
          Isentropic coefficient or ideal gas heat capacity ratio [-]
      P1 : float
          Upstream relieving pressure; the set pressure plus the allowable
          overpressure, plus atmospheric pressure, [Pa]
      P2 : float
          Built-up backpressure; the increase in pressure during flow at the
          outlet of a pressure-relief device after it opens, [Pa]
  
      Returns
      -------
      F2 : float
          Subcritical flow coefficient `F2` [-]
  
      Notes
      -----
      F2 is completely dimensionless.
  
      Examples
      --------
      From [1]_ example 2, matches.
  
      >>> API520_F2(1.8, 1E6, 7E5)
      0.8600724121105563
  
      References
      ----------
      .. [1] API Standard 520, Part 1 - Sizing and Selection.
      '''
      r = P2/P1
      return ( k/(k-1)*r**(2./k) * ((1-r**((k-1.)/k))/(1.-r)) )**0.5